STUDY BEST

Inverse Trigonometric function In  mathematics , the  inverse trigonometric functions  (occasionally also called  arcus functions ,   antitrigonometric functions  or  cyclometric functions ) are the  inverse functions  of the  trigonometric functions  (with suitably restricted  domains ). Specifically, they are the inverses of the  sine ,  cosine ,  tangent ,  cotangent ,  secant , and  cosecant  functions, and are used to obtain an angle from any of the angle's trigonometric ratios. Inverse trigonometric functions are widely used in  engineering ,  navigation ,  physics , and  geometry . There are several notations used for the inverse trigonometric functions. The most common convention is to name inverse trigonometric functions using an arc- prefix:  arcsin( x ) ,  arccos( x ) ,  arctan( x ) , etc. (This convention is used throughout this article.) This notation arises from the following geometric relationships:  When  measuring in radians, an angle of  θ radians will

Matrix In  mathematics , a  matrix  (plural:  matrices ) is a  rectangular   array  of  numbers ,  symbols , or  expressions , arranged in  rows  and  columns . For example, the dimensions of the matrix below are 2 × 3 (read "two by three"), because there are two rows and three columns: {\displaystyle {\begin{bmatrix}1&9&-13\\20&5&-6\end{bmatrix}}.} Provided that they have the same size (each matrix has the same number of rows and the same number of columns as the other), two matrices can be  added  or subtracted element by element (see  Conformable matrix ). The rule for  matrix multiplication , however, is that  two matrices can be multiplied only when the number of columns in the first equals the number of rows in the second  (i.e., the inner dimensions are the same,  n  for an ( m × n )-matrix times an ( n × p )-matrix, resulting in an ( m × p )-matrix. There is no product the other way round, a first hint that matrix multiplication is not  commutat

Differentiation Differentiation allows us to find rates of change. For example, it allows us to find the rate of change of velocity with respect to time (which is acceleration). It also allows us to find the rate of change of x with respect to y, which on a graph of y against x is the gradient of the curve. There are a number of simple rules which can be used to allow us to differentiate many functions easily. If y = some function of x (in other words if y is equal to an expression containing numbers and x's), then the  derivative  of y (with respect to x) is written dy/dx, pronounced "dee y by dee x" . Differentiating x to the power of something 1) If y = x n , dy/dx = nx n-1 2) If y = kx n , dy/dx = nkx n-1 (where k is a constant- in other words a number) Therefore to differentiate x to the power of something you bring the power down to in front of the x, and then reduce the power by one. Examples If y = x 4 , dy/dx = 4x 3 If y = 2x 4 , d